扩展体的经典电动力学
Classical Electrodynamics of Extended Bodies
摘要：
我们研究扩展体的经典电动力学。目前，在文献中还没有这样的机构的自洽动力学理论。电磁能量动量在电荷存在时不守恒，需要进行一些加法。到目前为止，发现的唯一有点合适的附加物是点电荷。这些都有无穷大的自能，需要一些重整化过程和微扰方法来解释辐射。我们回顾了导致理解这些事实的历史。然后，我们调查可能的自洽，非点电荷，经典电动力学理论。我们开始与拉格朗日只组成的里奇标量（重力）和标准电磁场拉格朗日，并考虑添加以外的点电荷及其相关的相互作用拉格朗日。在涉及电磁场张量的一阶导数的拉格朗日中包括二次项提供了足够的应力-能量项以允许能量-动量守恒。有三个这样的独立条款：一个直流电流的相互作用和两个曲率介导的（非最小耦合），短程相互作用，其中之一改变奇偶变换下的符号。这些可以被解释为非电磁的短程力。对于最简单的理论，只有度规和电磁势1-形式作为独立的场，我们发现一个单一的，稳定的，球形（自旋为0）的解决方案，由于在解决方案的中心可积奇点，量子化的质量和电荷。它的电荷小于数值误差，它的质量由拉格朗日中的一个新常数设定。它有一个小的中心电荷核，周围是一波交替带电的球壳，其中电荷密度波的振幅与径向坐标成反比。
英文摘要：
We study the classical electrodynamics of extended bodies. Currently, there is no self-consistent dynamical theory of such bodies in the literature. Electromagnetic energy-momentum is not conserved in the presence of charge and some addition is required. The only somewhat suitable addition found to date are point charges. These suffer from infinite self-energy, requiring some renormalization procedure, and perturbative methods to account for radiation. We review the history that has led to the understanding of these facts. We then investigate possible self-consistent, non-point-charge, classical electrodynamic theories. We start with a Lagrangian consisting only of the Ricci scalar (gravity) and the standard electromagnetic field Lagrangian, and consider additions other than point charges and their associated interaction Lagrangian. Including quadratic terms in the Lagrangian involving first-order derivatives of the electromagnetic field tensor provides sufficient stress-energy terms to allow for conservation of energy-momentum. There are three such independent terms: a direct current-current interaction and two curvature-mediated (non-minimally coupled), short-range interactions, one of which changes sign under a parity transformation. These could be interpreted as non-electromagnetic, short-range forces. For the simplest possible theory, with only the metric and the electromagnetic potential 1-form as independent fields, we find a single, stable, spherical (spin-0) solution, which due to an integrable singularity at the solution's center, has quantized mass and charge. Its charge is smaller than numeric error, and its mass is set by a new constant in the Lagrangian. It has a small, central core of charge surrounded by a wave of alternatingly charged, spherical shells, where the amplitude of the charge density wave is inversely proportional to the radial coordinate.
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